For the market, La Casa del Pueblo on Blue Island south of 18th Street.
For lunch, nsxtasy's suggestion of Nuevo Leon is a fine one. La Cebollita on Ashland south of 18th is another possibility.
there are also places which specialize in one thing: e.g. carnitas (Carnitas Uruapan on 18th near the L station), or birria (Birrieria Reyes de Ocotlan further east on 18th). But with a group it sounds like a place with a variety of things to choose from would be good.
Edit: I see Big Willi has some of the same suggestions!